Ordinary Differential Equations: Methods and Stability

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Related lectures (30)

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Convergence: Euler's Method

Explores stability and convergence in numerical methods for ODEs, focusing on Euler's progressive method.

Numerical Methods: Euler Schemes

Focuses on Euler schemes for numerical approximation of forces and velocities.

Euler Backward Method: ODEs

Explores the Euler backward method for ODEs, discussing stability, error reduction, and implicit vs explicit methods.

Elasto-gravity Bending: Mechanics of Slender Structure

Explores the deformations of an inextensible sheet bent under self-weight and its equilibrium shapes under gravity.

Explicit Stabilised Methods: Stochastic Differential Equations

Covers explicit stabilized methods for stiff stochastic differential equations, analyzing their properties and applications.

High Order Methods: Space Discretisation

Covers high order methods for space discretisation in linear differential systems.

Numerical Methods: Differential Equations and Stability Analysis

Covers numerical methods for solving differential equations and their stability analysis, focusing on error calculation and practical applications in engineering and science.

Exam Problems: Nonlinear Equations & ODEs

Covers exam-like problems on nonlinear equations, ODEs, and numerical methods.

Numerical Methods: Runge-Kutta Approximation

Covers the Runge-Kutta method for approximating solutions of differential equations.

Numerical Differentiation: Part 1

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.